Nonlinear thermoelastic topology optimization with the level-set method

Abstract

This work presents level-set topology optimization of structures considering nonlinear thermoelasticity. To analyze a structure experiencing large thermoelastic loads, a stress-free deformation driven by temperature change is introduced by multiplicative decomposition of the mechanical and thermal deformations. The consistent design sensitivity and the strategy of obtaining optimal update velocity are presented. By incorporating the thermoelastic nonlinear-ity into the optimization scheme, the design space is widened because of the increased accuracy of the structural and sensitivity analysis at the higher loading conditions. To demonstrate the effect of the nonlinearity in the context of large-deforming structures, the end-compliance minimization problems are solved for a range of thermoelastic loads. Changes in the layouts for a given load are shown and discussed with regards to their structural behavior. The material layouts are shown to be designed in a way that a counteracting effect between thermal and mechanical loads is created. We also demonstrate that such a manipulation of the thermal loading path suppresses the mechanical deformation even up to snap-through instability. To further elucidate the effect of nonlinearity, the nonlinear layouts and their behaviors are compared with those obtained from the optimization that considers linear thermoelasticity only.